DENVER—A bill to scale back strict Columbine-era school discipline policies cleared the first hurdle in the Colorado Senate, but it’s got a ways to go with lawmakers who think the legislation tries to do too much.

A Senate committee forwarded the bill on a 3-2 party-line vote with Republicans voting against on Thursday.

The proposal sponsored by Democratic Sens. Linda Newell and Evie Hudak would eliminate zero-tolerance policies, and expulsions would be mandatory only in cases where a student brings a gun to schools. Supporters say the goal is to give school administrators more discretion over student discipline.

But the bill also has new reporting requirements for law enforcement and schools. Some lawmakers say the requirements are cumbersome and that the legislation has become too complicated.